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Topic 4. Lecture 7. Inferring phylogenies
We established that all modern species originated from the same common
ancestor (LUCA). The next step is to reconstruct their phylogeny, i. e., to elucidate
the details of this process.
Just 40-50 years ago, there was a lot of pessimism on whether phylogenies will
ever be discovered with any confidence. Today, we are close to knowing the whole
Tree of Life, at least to the extent to which it is really a tree.
The hippopotamus is more
similar, at least at the level of
phenotype, to the pig, but is
more closely related to the
dolphin.
40 years ago, the common belief was that
great apes are more closely related to each
other than any of them to humans. This is
not true.
This work has been
performed at our
Department!
Land plants
originated from green
algae Charophyta,
and relationships
between their major
clades have also
been resolved.
There are two complementary reasons for progress in inferring phylogenies:
1) molecular data
and 2) sophisticated algorithms and software tools.
Indeed, a genome contains more traits than any higher-level description of the
organism. Also, one does not need to be a specialist in a particular group of
organisms.
Every segment of genomes contains a lot of phylogenetic information:
MSSHKTFRIKRFLAKKQKQNRPIPQWIRMKTGNKIRYNSKRRHWRRTKLG
MASHKTFRIKRFLAKKQKQNRPIPQWIRMKTGNKIRYNSKRRHWRRTKLG
MPSHKTFRVKQKLAKAQKQNRPIPQWIRLRTGNTIRYNAKRRHWRKTRLG
MPSHKTFRTKQKLAKAQKQNRPIPQWIRLRTGNTIRYNAKRRHWRKTRLG
MPSHKTFRIKQKLAKKQRQNRPIPYWIRMRTDNTIRYNAKRRHWRRTKLG
MPSHKSFMIKKKLGKKMRQNRPIPHWIRLRTDNTIRYNAKRRHWRRTKLG
vertebrate
vertebrate
fungus
fungus
plant
plant
Homo sapiens
Danio rerio
Neurospora crassa
Podospora anserina
Triticum aestivum
Arabidopsis thaliana
Alignment of amino acid sequences of ribosomal protein L39 from 6 species.
Red - informative trait states (shared within vertebrates, fungi, or plants)
Green - uninformative trait states (unique to a species)
Blue and Yellow - misleading trait states (shared by distant species, due to homoplasy).
To extract phylogenetic information from may of traits of many species,
sophisticated algorithms and powerful computers are necessary. However, the
basic ideas are simple.
The first question is: how can the phylogeny of a set of modern species be
described? Such descriptions are provided by phylogenetic trees.
A phylogeny can be described by a tree only if two key conditions are satisfied:
i) variation within each lineage can be ignored, and each cladogenesis was an
instant split,
ii) there were no secondary merging of lineages.
Violations of condition i) may become important only if we study very similar species.
Violations of condition ii) are very important for prokaryotes, where lateral gene transfer is
so common that we often encounter "phylogenetic networks", instead of trees.
Mathematically, a tree is a graph without cycles.
Terminology: The lineage which corresponds to the common ancestor is called
the ROOT of the tree; extant species (and, perhaps, extinct species which left no
descendants) are LEAVES; and intermediate ancestors are INTERNAL NODES; all
these are connected by EDGES. Two most closely related species are SISTERS,
any other is an OUTGROUP to them.
Complete branch = clade
Suppose that a phylogeny we study can, indeed, be represented by a tree.
A phylogenetic tree has two properties:
i) Each leaf carries a unique label - a leaf corresponds to a particular species!
ii) The tree is binary: each cladogenesis produces only two branches.
A trifurcation simply means that we cannot determine the order of bifurcations.
A phylogenetic tree describes how the common ancestral lineage branched off to,
eventually, form the set of extant species. The order in which different lineages
split is called topology of the tree, and topology is more fundamental than, say,
the relative lengths of different branches of the tree.
Top: 4 trees with the same topology.
Bottom: a tree with a different topology.
So, we have a set of N species that evolved from the common ancestor, and want
to discover their phylogenetic tree. How do we proceed?
A naive idea is to try all possible "substantially different" trees and to chose the
one which fits the data best. However, with N > 10-15, trying all possible trees is
impossible.
Discovering the phylogeny by trying all possible trees is an "NP-hard" (nonpolynomially hard) problem - because their number T(N) increases exponentially
with N. Obviously, there is just one possible tree for 2 species, so that T(2) = 1. We
can attach the 3rd species to this tree is 3 ways, so that T(3) = 1 x 3.
To each of the 3 possible 3-species trees, we can attach the 4th species in 5 ways,
so that T(4) = 1 x 3 x 5 = 15.
Five 4-species trees that can be built from the 3-species tree #1. T(4) = 15.
Thus,
T(N) = 1 x 3 x 5 x 7 x ... x (2n-3) = {1 x 2 x 3 x 4 x ... x (2n-3)}/{2 x 4 x ... x (2n-4)} =
= (2n-3)!/2n-2(n-2)!
When N increases, T(N) increases faster than any polynomial in N - that is why
considering all possible trees is an "NP-hard" problem.
Number of
Number of trees with nodes
Number of trees with nodes
species
not ordered in time, T(N)
ordered in time, O(N)
1
1
1
2
1
1
3
3
3
4
15
18
5
105
180
6
945
2700
7
10,395
56,700
8
135,135
1,578,600
9
2,027,025
57,153,600
10
34,459,425
2,571,912,000
100
~3.35x10184
~1.37x10284
1000
~3.81x102863
~3.02x104831
T(N) does not take into
account the temporal order
of events in different clades,
and O(N) does. We will
encounter O(N) later.
The same tree (T(N)) or
different trees (O(N))?
In addition to cladogeneses, a tree can also display changes of the trait states.
A phylogenetic tree based on a segment of a protein from Homo sapiens, Mus
musculus, and Rattus norvegicus. A phenotype consists of 6 traits, each
associated with a position within the alignment. Actual phenotypes of the 3 extant
species and the inferred phenotypes of the common ancestor of mouse and rat
and of the whole set are shown, together with evolutionary events. Traits 1 and 6
are invariant and, thus, of no help.
So, we cannot simply try all possible trees and see which one of them fits the data
best (even if we know how to evaluate this fit). What can we do instead?
Let us start from two simple cases when reconstructing a phylogeny is easy:
I) Purely divergent evolution, without any homoplasy - as revealed by lack of
pairwise conflicts in the matrix of traits (hierarchical joint distribution).
II) Constant-rate evolution (or evolutionary clock) - as revealed be identical
distances from any two sisters to the outgroup.
DIFFICULT MATERIAL FROM HERE!
Trait 1
Trait 2
Trait 3
Species 1
Species 2
Species 3
Species 4
Species 1
0
0
0
Species 1
0
0.3
0.8
0.8
Species 2
0
0
1
Species 2
0.3
0
0.8
0.8
Species 3
1
0
1
Species 3
0.8
0.8
0
0.2
Species 4
1
1
1
Species 4
0.8
0.8
0.2
0
I) Matrix of traits, consistent with
purely divergent evolution
II) Matrix of distances, consistent
with constant-rate evolution
Special case I. Reconstructing divergent evolution.
Theorem. If a set of species originated from the common ancestor by (exclusively)
divergent evolution, the phylogenetic tree which describes this evolution is
maximally parsimonious (i. e., involves the minimal possible number of changes).
Proof. Obvious - a tree which involves more than the minimal number of changes
must involve some homoplasy (repetitive origins of the same trait state).
Without homoplasy, a derived trait
state always define a clade.
Synapomorphy is a fancy word for
such a shared derived trait state.
OK, but how do we know if evolution of our set of species was divergent? We
already know the answer: if the joint distribution of traits contains pairwise
conflicts between traits, evolution must involve homoplasy. In contrast, if this
distribution is hierarchical, the hypothesis of exclusively divergent evolution is
not rejected - and is probably true.
Species 1
Trait 1
0
Trait 2
0
Species 2
0
1
Species 3
1
0
Species 4
1
1
Conflict between two traits.
We need only to make one last step - to produce the maximally parsimonious tree
from a hierarchical matrix of traits. There is a simple algorithm for this (traits are
binary):
1) Choose a trait with the minimal number of species having the derived state (if
more that one trait has this number, choose any one). Take all species which
possess the derive state - they form the lowest-level clade.
2) Forget about the trait just used, and repeat this procedure, until all the traits are
used.
Let us see how this works:
Venn diagram representing the same data. For each trait, species with the trait
state shown in red in the table are enclosed into a line of the corresponding color.
Let assume that these states are derived. Trait 116 in involved in two conflicts - we
will ignore it.
Let us remove trait 116. After this, the algorithm can be applied. This is one of
several maximally parsimonious trees that are consistent with our matrix of traits
(minus trait 116). Find other possibel MP trees.
If several different trees are equally parsimonious, each of them can be used - we
cannot know which one is correct.
A phylogenetic tree reconstructed using the above matrix of traits, ignoring trait
116. Only the phenotype of the last common ancestor is shown, but phenotypes of
all the intermediate ancestors have also being reconstructed.
Above, we assumed that we know, for each trait, which state is ancestral (or
primitive, or plesiomorphic) and which is derived (apomorphic). For this, several
methods can be used:
1) Rely on partial a priori understanding of evolution: for example, vestigial eyes
or an inserted pseudogene or a TE must be derived states (why?).
2) Rely on fossils: trait states that appear later in the fossil record (e. g., wings of
birds), must be derived.
3) Rely on an outgroup - one or several species that definitely branched off before
the series of cladogeneses which we want to reconstruct. How do we know that
something is an outgroup? By assuming approximately constant rate of evolution
- mice are certainly an outgroup for humans and chimpanzees. Then, for a trait
that is variable within the set of species we study, its state present in the outgroup
is probably ancestral, as long as the outgroup is not too far away.
Mus must be an outgroup to hominids! Drosophila is also an outgroup to
hominids, but much less useful. So, an outgroup must be not too close but also
not too distant.
4) A more fancy approach: first, construct an unrooted tree, without knowing
which traits states are derived (this is only slightly more complex than what we
did), and then root the tree. The number of unrooted trees U(N) = T(N-1) - still a lot
for large N, but unrooted phylogenies start from N = 4. There is only one unrooted
tree of 3 species, and 3 unrooted trees of 4 species.Of course, an unrooted tree
does not contain full information about past evolution.
One possibility is to assume near-constant rate of evolution, and root the tree in
the middle.
OK, but what to do if we there are many conflicts between traits? If all conflicts
are due to a small number of "bad" traits, these traits can be ignored, and
hierarchy restored. However, multiple conflicts prove that evolution of the set of
traits was significantly non-divergent.
In this case the maximally parsimonious tree is not a solution, because:
a) this tree is hard to find - generally, this is an NP-hard problem.
b) this tree may not correspond to reality - why to expect minimal homoplasy?
Here a different approach is worth trying, which works in the other special case.
Special case II. Reconstructing constant-rate evolution.
Suppose that we have data on a large enough number of traits, and that evolution
of our set of species occurred at a constant rate (evolutionary clock).
If so, the distance between phenotypes of two species immediately tells us how
long ago their lineages split. Thus, a symmetric NxN matrix of distances between
our N species can be immediately converted it into their phylogenetic tree.
Let is convert the above matrix of traits into the symmetrical matrix of distances
between the species. The distance is the number of traits in different states.
Here, the number of traits is too small to assume constant-rate evolution.
A more suitable example: matrix of distances between second introns of beta
actin gene from human Homo sapiens, chimpanzee Pan troglodytes, orangutan
Pongo pygmaeus, rhesus macaque Macaca mulatta and common marmoset
Callithrix jacchus.
Hs
Pt
Pp
Mm Cj
Hs
-
Pt
2
7
16
52
-
6
16
44
-
23
61
-
50
Pp
Mm
Cj
-
The phylogenetic tree can be recovered from the matrix of distances using an
algorithm UPGMA (Unweighted Pair Group Method with Arithmetic mean):
1) find the most similar pair of species;
2) replace these two species with a clade consisting them. The distances
to this clade are arithmetic means of distances to the two removed species.
3) repeat this procedure.
Hs-Pt
Pp
Mm
Cj
Hs-Pt
Pp
Mm
Cj
-
6.5
16
48
-
23
61
-
50
-
The distance matrix after the first step of UPGMA. Naturally, N-1 steps are needed
to construct the tree, rooted at the middle. Here similarity = relatedness.
However, appliyng UPGMA when evolution was not constant-rate can lead to
errors.
Hs
Cf
Mm
Hs
Cf
Mm
-
0.35
0.56
-
0.63
-
Matrix of distances between human Homo sapiens, dog Canis familiaris, and
mouse Mus musculus. Here, the distance is the estimated per site number of
synonymous nucleotide substitutions.
A wrong tree obtained from this matrix by UPGMA (left) and the true tree (right).
Analogously to Case I, a simple test can tell whether our data are consistent with
the assumption of Case II. The evolutionary clock hypothesis implies that
distances AC and BC must be equal (where C is a definite outgroup for sisters A
and B). This is a powerful test!
A
B
C
A
B
C
-
10
30
A
-
30
B
-
C
Evolutionary clock possible
A
B
C
-
10
25
-
35
-
Evolutionary clock impossible
Often, data FAIL both tests - there are conflicts, and distances from sister species
to the outgroup are not the same - revealing that evolution was not exclusively
divergent and did not proceed at an exactly constant rate.
What to do? More sophisticated approaches can be used.
Maximal likelihood - chose the hypothesis H (tree) which generates the data D
(matrix of traits) with the highest probability Prob(D|H). This quantity is also
known as the likelihood of the hypothesis, given the data. However, to calculate
Prob(D|H) we need to have some idea of how evolution occurred - for example,
that some traits evolve faster than others.
Bayesian methods – extension of the previous approach, under assumption that
we have some a priori idea of what trees are more probable.
Things get technical at this point.
However, the best solution is to find better traits, variable enough to convey some
information on evolution, but still not producing homoplasy often. Such traits do
exist, for each depth of phylogeny.
Homoplasy is the worst enemy of phylogenetic reconstruction!
How to find good traits for phylogenetic reconstructions?
1) Phylogenies of very similar species can be based on substitutions at individual
sites of junk DNA.
2) Phylogenies of moderately similar species canbe based on short inversions:
AAACGAGGGAAA > AAACCCTCGAAA
Indeed, two independent inversions will rarely have the same boundaries.
Inspect pairs of columns, and look for all 4 possible combinations of red and
green - are there any conflicts?
3) For yet more distant species, traits associated with gene orders can be used.
4) For very distant species, only tratis associated with sequences of conservative
proteins can be used, and in this case homoplasy cannot be ruled out.
Nikaido et al. PNAS 1999
Aguinaldo et al. Nature 1997
Wolf et al. 2004
Irimia et al. 2007
Rogozin et al. 2007
OK, but are phylogenies trees?
Non-zero width of edges should sometimes be taken into account, because it can
lead to "lineage sorting", but this is not a big deal at the Macroevolutionary scale.
Even in eukaryotes occasional episodes of lateral gene transfer (LGT) are welldocumented. Still, eukaryotic phylogenies are generally tree-like. In bacteria, LGT
is pervasive, although there still is a tree-like "phylogenetic signal".
OK, but are phylogenies trees?
1) Non-zero width of edges, i. e. within-lineage variation, needs to be taken into
account if variation can persist between successive cladogeneses (bottom row).
The subsequent random loss of such persistent variation can make phylogenies
of some loci incongruent with the true phylogeny of lineages. This is the case for
~1% of loci, in the case of (gorilla, (chimpanzee, human)) phylogeny. However, this
may become a problem only when less than ~1,000,000 generations occur
between successive cladogeneses.
2) The other complicating factor, post-cladogenesis genetic exchanges, is
common in some groups of organisms and essentially absent in other groups. In
particular, phylogenies of many prokaryotes are more like complex networks,
instead ot simple trees, due to pervasive lateral gene transfer.
Post-cladogenesis genetic exchanges can be detected by the ABBA/BABA test:
1) Construct the phylogeny of a quartet of species as if it were a tree (let us first
assume that it consists of 2 pairs of sisters),
2) For traits which display parallel divergence within both pairs, count the
numbers of ABBA vs. BABA traits,
3) If these numbers are similar, there is no reason to suspect exchanges.
Otherwise, they are likely - because selection can hardly lead to correlated
divergences within different pairs.
The same reasoning can
be applied to the other
kind of phylogeny of a
quartet.
W.F.Doolittle 2000
Sci Am
W.F.Doolittle 2000
Sci Am
2001
Nature
Why do we care to know phylogenies?
First, because,
this is something
we want to know!
Second, hard-todiscover
phylogenetic
affinities can be
really important.
Comparing phylogenies can reveal patterns in coevolution.
Phylogenies of
primates (left)
and their malaria
parasites (right).
Phylogenies can reveal past
changes in geography.
Phylogenies are important not only in
biology. Ohylogeny of Indo-European
languages; numbers indicate inferred
times of divergence.
Thoughts about classification (you can safely forget them)
Any classification somehow reflects similarity between the objects we
classify. However, not all classifications are hierarchical. For example, the
periodic table of elements is not hierarchical, and does not reflect
common ancestry. This is because chemical properties of atoms can
change radically after a single event: 40K decays into 40Ar.
In contrast, classification of species (at least of eukaryotes) is hierarchical,
because evolution is slow and gradual, and common ancestry strongly affects
similarity.
The only contentious issue is whether it is OK to use paraphyletic taxa. Can we
say dinosaurs, or only non-avian dinosaurs (when we want to exclude birds)?
monophyly (holophyly)
polyphyly
paraphyly
My answer to is "who cares"? A classification cannot be true or false - it can only
conform (or not conform) to some set of rules. In contrast, a phylogeny can be
true or false. The only real issue is to discover the true phylogeny - and how we
describe it using the language of classification is not important.
Conclusions about phylogenetic reconstructions:
1) In eukaryotes phylogenies are mostly trees, in prokaryotes LGT is very
common.
2) In simple cases we can easily find the correct tree, assuming either exclusively
divergent or constant-rate evolution.
3) If neither of these assumptions is consistent with the data, we can either use
more sophisticated methods or, preferrably, seek better traits, not prone to
homoplasy.
4) A lot of phylogenetic relationships have already being elucidated, and the
whole Tree of Life will be known soon.
Quiz: consider this matrix of traits:
Traits:
Species:
1
2
3
4
5
6
A
0
1
1
0
0
1
B
1
0
0
1
1
0
C
0
1
1
0
0
0
D
0
0
1
0
0
0
E
0
0
0
0
1
0
F
0
0
0
1
1
0
Is this matrix consistent with exclusively divergent evolution?
If not, home many traits are responsible for homoplasy?
Construct the phylogenetic tree, assuming that 1 is always a derived state.